Interactions between light and hypersonic waves can be enhanced by tight field confinement, as shown in periodically structured materials(1), microcavities(2), micromechanical resonators(3) and photonic crystal fibres(4-6) (PCFs). There are many examples of weak sound-light interactions, for example, guided acoustic-wave Brillouin scattering in conventional optical fibres(7). This forward-scattering effect results from the interaction of core-guided light with acoustic resonances of the entire fibre cross-section, and is viewed as a noise source in quantum-optics experiments(8). Here, we report the observation of strongly nonlinear forward scattering of laser light by gigahertz acoustic vibrations, tightly trapped together in the small core of a silica-air PCF. Bouncing to and fro across the core at close to 90 degrees to the fibre axis, the acoustic waves form optical-phonon-like modes with a flat dispersion curve and a distinct cutoff frequency Omega(a). This ensures automatic phase-matching to the guided optical mode so that, on pumping with a dual-frequency laser source tuned to Omega(a), multiple optical side bands are generated, spaced by Omega(a). The number of strong side bands in this Raman-like process increases with pump power. The results point to a new class of designable nonlinear optical device with applications in, for example, pulse synthesis, frequency comb generation for telecommunications and fibre laser mode-locking.